A bicycle odometer (which measures distance traveldb eb5ps kx (3i8-c5peed) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with8pd(b s5x-ei 5ckb3e p 24-inch wheels?

Suppose a disk rotates at constant angular veloc.jd- as54m tfn:m lu5rity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the pointjarl s-ud4t.m nm55 :f have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the angular veloh)(4 h-wby3nkc * vq.gcx udd7city $\omega$ Explain.

Can a small force ever exert a greater torqu,guugrw x4c6thq 0k se:(nzub *d )u9*e than a larger force? Explain.

If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.

Why is it more diffib7pk xd9mn6u5+m)j /zssq :mo cult to do a sit-up with your hands behind your head than when your arms are stretched out in front of you? Asb 5mxpm z9m o)d: q+6u7kj/ns diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at the peddl( w*pre2j5yk :sp o/al cranks. In wh5(o jsp rkpd/yw :e2*lich gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs with flesx t*9z+yp k ( qzdj*fc-zw2p2fh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distrdzp**tf p9wfc (+k2x 2-jqz yzibution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow bl g .z0j.zkbd+6aka/leam?

If the net force on a system is zely.l.(*7nr so) cusgq ro, is the net torque also zero? If the net torque on a syu(lro .*ss y7)qgcn. lstem is zero, is the net force zero?

Two inclines have the same height but make different angles with the horig x/159rq eh4nfp1gpc11xf wnzontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Expla1/qnh rw11 ggf ep9pfcx54 1xnin.

Two solid spheres simultaneously start rolling (from rest) dow yqtke *86gb 5u84)3inzccrs bn an incline. One sphere has twice the radius and twice the mass of the other. Which reachezb8t)6csun iq3c* gebk8yr45s the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mkn v k:om md;i5e7n*l.ass. They start from rest at the top ondlnom.;5i * v:ekm7k f an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserveo tsci5e * 6;*;-dbsackp mb,jd. Yet most moving or rotating objects eventusm6-bs,p 5c;;*ij tb *ec okadally slow down and stop. Explain.

If there were a great migration of people toward th gfv6,mmhbj/ (.i ee5ie Earth’s equator, how would this affect the length ofghj ,.fim/(5v embi6e the day?

Can the diver of Fig. 8–29 do a somersau3f2cvp qjba+ 2o,de6f lt without having any initial rotation when she leaves the boa2vbda+ fjfo62 q,c3 eprd?

The moment of inertia of a rotating solid disk mw*h vph.:(xc about an axis through its center of mass .x (c:hv*whp mis $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-p6i;i *pw4hplcq u0h;8iq b2gkg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? E08p4 hqp6 hpu2i;lc q*gi; wbixplain.

Two spheres look identical and have the same mass..t6lgm lq2g msv*w3 qv4;iqt * However, one is hollow and the other is solid. Describe an evm2l qq3;v mqstgi4 .g **wlt6xperiment to determine which is which.

The angular velocity of a wheel rotating;jx mj:4zn xn5hfc s23 on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential lineh x2534njf:sm xj; cnzar acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntab-o.ed g, rqpg(le. What hdo.gr- (gqp,eappens if you walk toward the center?

A shortstop may leap into tbri /lc2ex/v5v 4 bcj+r7 i2r2k gxci3he air to catch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and lvibg j74xrvl cc2 i2 e5br+3/r k/2cixegs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law odc,u5 mldp( 4-(l aedpf conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.l,c4u e d-mddl(ap(5p

  Express the following angles in radix-38v c .xr:uv4vvu mians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amahvf: +i3ti/.v2u, ebja str8pzing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (ii, v/2s8phatb:.+uivret fj 3n radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directedeh ss lmdi2bkj; 1/s3. at the Moon, 380,000 km from Earth. The beam diverges at an an db si3jh;e2l/kms1s. gle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When the motor is turnt n9 8:lphas-xed off during operation, s :tlxanp-89 hthe blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the ball makpo)lb80e*u6iabr 0nm a;jz o5es 15.0 revolutions, what is i);8aeo5ina *pbbl6zm u0or 0 jts diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How manyng1*a/ sc1s lk revolutions do the wheesa/l 1nks*1cg ls make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm.8w3 2sg m hv9s30j.:otd:tlhwa ;boez Calculate its angular velocittohssmtv ha3 9l 3j.bo w8z20:wd;e:g y in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revol4k /joh(u a1i,o2x kieution in 4.0 s (Fig. 8–38). (a) What is the linear speed( k/oh4jeau2i xi1o, k of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Efykjsiyfcz3my ) -5;n7( a 2ooarth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of as+j a*v ai5rms;7rkoc 3kf2f* point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) mud 5 n:hxdj:k rbxoa;.1st a centrifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration ofon;.xdha: j d1r kbx:5 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its+3obhi 97kjejo cl:y( center from 130 rpm to 280 rpm in 7:kej3(cobl hy +io j94.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radiuqh1cz zn/07x ymxevv/ 5:ld,z s $R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, asn16k nmf eoj4-b, uzy)b)7kn ttronauts aboard the Apollo spacecraft put themselves into a slow rotation to di6 e)bonynm)-74bk,1nf kjuztstribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 220 sbtd z(-8 s )ad)x8hsip. Through how mani pt-)a)(xhsds 88bz dy revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s,y17 qdzhtu;k. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested jp95 m deoe8e)n+85flj 7mudjh9qy+ifor the stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn the5ie8ye 9oqj+ fn5dpm7 j dh 9m)+luj8rough 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 360 rpm ins+gx c:;8- nvf((e ztruc5hob 6.5 s. How far will a point o(f-+vuxbsr :c;5ec oh ( n8gtzn the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is ri a)mdvg/+ 14sjny h-yunning at 850rev/min It turns 1500 revolutions before i1ni +aj-vy)/y gmd4hst comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 regqb mfh2 055qevolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter 2bfmgqqe 5 05hof 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65vnmpretpk:-o-v s8k.v3bufe0, (y n8 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter ofer s p( -k-3:mknyvvon,et 0bpu. v88f 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal when climbingrsh dh 7 vr0k+s(a8zj+bvy 8,w a hill. The pedals rotate in a+hj k+(ah8y08sdzvr vs bw7,r circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end o*lvmy0f2bo u4b dw4 et6)3q qaf a door 74 cm wide. What is the magnitude oob d4e0b32q u)*myfvl w4 tqa6f the torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig. 8–39. Assuwa/cmpq:t8 9 vge c-1qys 17yxme that a friction torq1tc7xpaw:sq m9g yy- q/1e8vcue of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached wd4l w80syy n6c, bv*wxl6wt+ efo 8u)to the ends of a massless rod which pivo)0vy w 8+*l8t, 64 ufyl w6onwcxsdebwts as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a t5qe l2vv wps9/d 10mjforque of 380s1 fv pm wel9/52dvqj $m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radius 0.648 m w1sqs ow-52s td)7 xs-ua f4icjhen the axi2qxd4f a-5tcs1js7o ) u- sswis of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycl yoiuv1f/9)m se wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (why y/vuf)19i som?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, li8pel(nsu ;2hj ght rod is rotated in a horizontal circle of radius j puesnh8;2l (1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at constant angular y il/jejti-,3 speed (Fig.et-/jili ,jy3 8–42). The friction force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of 5p 1f.jidv,ftinertia of the array of point objects shown in Fig. 8–43 abouti 1df. pfjv5t,
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whose total mass isnnw-ii 0i32:ybqy+ (sz b2ntd $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the correct rate, engz.yz+ zm0/mw fineers fire four tangential rockets as shown in Fig. 8m/+. zwz0zmf y–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cy )w iw 9 0/yhrq8liezgo4ods3+linder with a radius of 8.50 cm and a mass of 0.580 kg. Calculate dqwoy 8ii3whl)40/og9er zs+
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelz+rah6 aty5i9 erating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on . xnkf w692xgi-5 azraa small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two ch-.ifag9xk6xr anw 5z2ildren (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eo-7i)+x9yqm e0v/q apl7wyc wventually brought uniformly to rest by a frictional t9yi+w pe-cqxway m07v q o/l)7orque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accew 7nus2 pu;/stlerates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely +60uc tx oiw4fby the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. Txt60u iw fo+4che ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as shown in Fig. 8–ub -de 6tx( d96*)e 8 y2kmo/ekitfiut46.f(oiu k)t2eb9kx68tdd 6meti -u/y *e
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine c8f vuxa3 9nm4donsists of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within four full turns (rev9p 7j hh8mzahg;(n c3oogo78hah nh z( p3;cmj9lutions) and releases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of mz:h0p+2rm+/kt fk(/ wo mv rwinertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque of 280,; q5seql lsr+2g6zi pkjuy84 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls wi d+igkt-k 2(( fpwqn,ythout slipping down a lane at 3.n (+pd f-q(y2iktwgk, 3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to thekko x+;gph:) v)w 2mqgri) xe+ncy +-y Sun as the sum of two terms,r+2 evp+ xi+-go)k)); qhcnmxwy: gyk
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radiu8ds uyq0v5nt a jpl4qt*335l js of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder. aj503*pt4 sq5ljyl qvnd3tu8    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls without smrf wca brqstf rx n* *q5g2qbh.:q*.)-, l1avlippinqvt 1cgbn* *qh:aw2-r*bf.famr )qlsqxr .,5g down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

  Two masses, $m_1$ = 18 kg and $m_2$ = 26.5 kg are connected by a rope that hangs over a pulley (as in Fig. 8–47). The pulley is a uniform cylinder of radius 0.260 m and mass 7.50 kg. Initially, is on the ground and $m_2$ rests 3.00 m above the ground. If the system is now released, use conservation of energy to determine the speed of $m_2$ just before it strikes the ground. Assume the pulley is frictionless.    $m/s$

  A 2.30-m-long pole is balanced:6uwmoa1ya 7oo6vicir n )62q /-edkw vertically on its tip. It starts to fall and its lower end does not slip. What will beiy2ko/or 6 m)- a1anvo6wc wi:7 ud6qe the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the b5fq,bc(eir xzu 4r11end of a thin string in a circle of radius 1.10 m at an angula4xz,er5c f(bri1 bu 1qr speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum ofval m 15zog2-x a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500lxg1m5-v2zo a rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a plbty4a0f+ wmkn gz6 k67atform that is rotating at a rate of 16t kmb7kgay6z0w4+fn.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can rylf2 e;rvomy7j89, :1ieu4sx f)x7t yt- hof qeduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is h o4jy 2 :i)yfmq1s-7,xev97xtor tf8fulyhe; er angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate froa4fnly9j0 9/uzb f kl(m an initial rate of 1.0 rev ebf9j0zanklf 9lyu 4 /(very 2.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertic( 6iqh2 b3ziazal axis through its center at a frequency of 1.5rev/s The wheel can be considered a uihz2z6bi (3a qniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning at 3,jeg hc;ir227vrl t* n.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of thml 81/o9 b6;3fozfzi,5ys ztufz u2khe Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$

(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk 7.sf8d bpbb*18 m,bsf n y3feitmgk,-of moment of inertia I is dropped onto an identical disk rotating at ang b i b1fgtkn .fsfbempy,78*s-,8db3m ular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns a- 1w c 31ea:wotqs5d(cr u*bb ,qqkaq7t 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the cenl d i6at.s,o v k1i89zg7je gd *bw.evjo9i38iter of a rotating merry-go-round platform oe 8aioi iige8 v913dj.zgboj*.6,sdv7 w 9 ktlf radius 3.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an angukrhjmqo8c6;g/w+v 6n lar velocity of 0.+ck/mvnho rg; 8qw6j68 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventunh ; y* n.zk58uom.pp dm *oi5z7c-jsually collapses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away n5.8k7dzm*j.u mopunzip -;*5hn oc y so angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds inqcl9 a 8,rz uw2be;,to dz;fdc1-b/pz excess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass / .5pd;i)y lydzdh 1thql-:j j$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, that ei6dd5s q 2y.zcan rotate freely without friction. The moment of inertia of the person plus the platfor zd2iyed. qs56m is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of aavqk/v iv 0-5gs*ax+a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of/i+5qxasavv0v a-gk * inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of jagaejf0j:- 1 the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unf:j 0ejj-gaa1winds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same sid/ hhzn)5f6wure always faces the Earth. Determine the ratio of the M 5r6znh)h /fuwoon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a ra-mz9ca: iy dcy*n;q; hca*a mj3:fjm5 te of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of ran(/u(fde 8lx odius 0.20 m acquires a rotational rate of from rest over a 6.0ndfle8u((x/o -s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylind;o),2cpcl x bp1et(ekgad 7k 0rical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reac0c a lb7ok)1t (xde2g,ce;ppkhes the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the anguln0gb5 27vfo ;kn ,if gvm*rx;iar speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as gream4g kby.6+z/mnb t *m l-id 5.oxxtur*t, were rotating at a speed of 1.0 revolution every 12 days. If it were to dmtm*mxt6g4oxui.rz+ 5- l/*. bnbykundergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobidg* 4 ejckh6(z 8quz1gle is for it to use energy stored in a heavy rotatihquc z *g814( jgd6zekng flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates anu:ltfk(1u:u f3o g:xm d;( n0wwvn,zq $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surface 1tfoe9 5gm7 qh8x jf)fat speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass 2a p edg8yw- ln7 qcdu:utc704*sfr.k M and length L can pivot freely (i.e., we ignore friction) about a hinge atta kq8ncud-4:td0al*gr. cfwe7yup s27ched to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radi 0e.0z ;mgbntbus R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that ite 0bgbmt;0.n z will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a tur(s-( prg+ djl igr1ppds 8:9oxn with a r(- prlsordig(j:8d+1 p xsg 9padius The forces acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a bval +3czv*9hrg .wih(.t e9 ssling of length 1.5 m and begins whirling rlg. 9ht39eih.+*wza scbv v(the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a souux p:s 32sjyrn4 6. k,pa-jjslid cylinder and her arms as thin rods, making reasonable estimates fur,s6 jj3 -apsu pxny4j.k2s :or the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly wuw/dqkq0p6 z2m sb+3 u9fhnw3hich consists of two cylindrical plates, of mass2+h mnu9 3dk/f03ubw 6wqzpq s $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rougqq/cseb72hbm.el ( p.h track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leavpehb /2lesqm(7qbc . .ing the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not y)od(vlds: ax dfeea429nio90 6:lu nassume $r\ll R$ h =    (R-r)

  The tires of a car make 85 r04 r dky)wsld4evolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire04ld4yk sdwr)? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s